As is well known, the construction of a desalination apparatus with a reverse osmotic membrane module is such that, as shown in FIG. 1, the reverse osmotic membrane module U is adapted to separate permeate water (pure water) WP from raw water (seawater) WF that is pressure-fed by a pump PM through a permeable membrane M, concentrated water (concentrated brine) WB being finally discharged from an outlet valve V2. In this kind of desalination apparatus, a gel layer G (FIG. 2) is formed on the permeable membrane M by contaminants, microbes or the like in the water over a long period of operation and thus the membrane performance or permeation performance deteriorates. It has thus been the practice to recover the permeation performance of the permeable membrane M by closing valve V1 at predetermined intervals of time T1 (once a month in the example shown), as shown by a dotted line A in FIG. 3, the gel layer G on the surface of the permeable membrane M then being dissolved and removed with a liquid chemical. Such removal operation is ordinarily performed at a given frequency within the range of from once every half a month to once every two months, depending on the specific operating conditions, such as the quality of raw water, the recovery rate, etc. Such being the case, certain problems are encountered since not only must the system be shut down, but also the cost of the liquid chemical and labour involved are considerable. These problems lead to an overall increase in the cost of the desalination.